I'm reading Sawyer's Prelude to Mathematics, from page 34-35:
[...]Prove that, if¹
Then the fractions just given are both equal to:
This question has a very definite form, and obviously to hammer it our by a lengthy and sharpless calculation, while veryfing the result, would bring one no nearer to the heart of the question. What interested me most was the question was the question, how did the examiner come to think of this question?
The pattern of the question includes the following aspects, $ac-b^2=0$ is the condition for the three quantities $a$, $b$, $c$ to be in geometrical progression.
1 - It is assumed that $b$ and $c$ are unequal. The text does not discuss this point, as it's not relevant to the main theme. What suggested the question to the examiner.